Acta Mechanica

, Volume 229, Issue 10, pp 4017–4031 | Cite as

Natural frequency veering and mode localization caused by straight through–cracks in rectangular plates with elastic boundary conditions

  • Tianming Huang
  • Huancai LuEmail author
  • D. Michael McFarland
  • Wen L. Li
  • Chin An Tan
  • Lawrence A. Bergman
  • Jian Gong
Original Paper


A solution method is presented for vibration analysis of through-cracked rectangular plates. A domain decomposition technique is employed in combination with a set of admissible functions which were previously proposed for triangular and rectangular plates with elastic boundary conditions. The continuity conditions at interconnecting boundaries of the subdomains are enforced by translational and rotational springs with zero or infinite stiffness. The Rayleigh–Ritz method is employed to determine the generalized coordinates and the corresponding modal frequencies and shapes. This special set of admissible functions allows all the involved integrals to be calculated analytically in closed form. Numerical examples are presented for plates with various crack configurations and boundary conditions. The current results are compared with those available in the literature to verify their convergence and correctness. The main advantage of the proposed method lies in its applicability to various combinations of boundary conditions and crack configurations. This method is then employed to determine the modal characteristics of simply supported square plates by focusing on the effects of various crack parameters on frequency veering, mode splitting, and mode localization. Finally, experiments are reported for three rectangular plates with different cracks for validation.


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This research was supported by the Ministry of Science and Technology of China through Grant No. 2017YFC0306202, the Department of Science and Technology of Zhejiang Province through Grant No. 2018C04018, and the National High-end Foreign Expert Foundation of China through Grant No. GDT20173300032.

Supplementary material

707_2018_2195_MOESM1_ESM.pdf (192 kb)
Additional Convergence Study Data


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  • Tianming Huang
    • 1
  • Huancai Lu
    • 1
    Email author
  • D. Michael McFarland
    • 1
    • 2
  • Wen L. Li
    • 3
  • Chin An Tan
    • 4
  • Lawrence A. Bergman
    • 2
  • Jian Gong
    • 1
  1. 1.Sound and Vibration Laboratory, College of Mechanical EngineeringZhejiang University of TechnologyHangzhouChina
  2. 2.Department of Aerospace EngineeringUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  3. 3.Advanced Information ServicesFenghua District, NingboChina
  4. 4.Department of Mechanical EngineeringWayne State UniversityDetroitUSA

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